A Michigan study concerning preference for outdoor activities used a questionnaire with a six-point Likert-type response in which 1 designated "not important" and 6 designated "extremely important." A random sample of n1 = 41 adults were asked about fishing as an outdoor activity. The mean response was x1 = 4.9. Another random sample of n2 = 50 adults were asked about camping as an outdoor activity. For this group, the mean response was x2 = 5.7. From previous studies, it is known that ?1 = 1.6 and ?2 = 1.5. Does this indicate a difference (either way) regarding preference for camping versus preference for fishing as an outdoor activity? Use a 5% level of significance. Note: A Likert scale usually has to do with approval of or agreement with a statement in a questionnaire. For example, respondents are asked to indicate whether they "strongly agree," "agree," "disagree," or "strongly disagree" with the statement. (a) What is the level of significance? .05 State the null and alternate hypotheses. H0: ?1 = ?2; H1: ?1 ≠ ?2 (b) What sampling distribution will you use? What assumptions are you making? (A) The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. (B)The Student's t. We assume that both population distributions are approximately normal with known standard deviations. (C)The standard normal. We assume that both population distributions are approximately normal with known standard deviations. (D)The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. What is the value of the sample test statistic? (Test the difference ?1 − ?2. Round your answer to two decimal places.) Find (or estimate) the P-value. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to the P-value. (if you can) (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ?? (A) At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (B)At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. (C)At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. (D)At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. (e) Interpret your conclusion in the context of the application. (A) Reject the null hypothesis, there is insufficient evidence that there is a difference between mean response regarding preference for camping or fishing. (B) Reject the null hypothesis, there is sufficient evidence that there is a difference between mean response regarding preference for camping or fishing. (C)Fail to reject the null hypothesis, there is insufficient evidence that there is a difference between mean response regarding preference for camping or fishing. (D)Fail to reject the null hypothesis, there is sufficient evidence that there is a difference between mean response regarding preference for camping or fishing

A Michigan study concerning preference for outdoor activities used a questionnaire with a six-point Likert-type response in which 1 designated "not important" and 6 designated "extremely important." A random sample of n1 = 41 adults were asked about fishing as an outdoor activity. The mean response was x1 = 4.9. Another random sample of n2 = 50 adults were asked about camping as an outdoor activity. For this group, the mean response was x2 = 5.7. From previous studies, it is known that ?1 = 1.6 and ?2 = 1.5. Does this indicate a difference (either way) regarding preference for camping versus preference for fishing as an outdoor activity? Use a 5% level of significance. Note: A Likert scale usually has to do with approval of or agreement with a statement in a questionnaire. For example, respondents are asked to indicate whether they "strongly agree," "agree," "disagree," or "strongly disagree" with the statement. (a) What is the level of significance? .05 State the null and alternate hypotheses. H0: ?1 = ?2; H1: ?1 ≠ ?2 (b) What sampling distribution will you use? What assumptions are you making? (A) The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. (B)The Student's t. We assume that both population distributions are approximately normal with known standard deviations. (C)The standard normal. We assume that both population distributions are approximately normal with known standard deviations. (D)The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. What is the value of the sample test statistic? (Test the difference ?1 − ?2. Round your answer to two decimal places.) Find (or estimate) the P-value. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to the P-value. (if you can) (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ?? (A) At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (B)At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. (C)At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. (D)At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. (e) Interpret your conclusion in the context of the application. (A) Reject the null hypothesis, there is insufficient evidence that there is a difference between mean response regarding preference for camping or fishing. (B) Reject the null hypothesis, there is sufficient evidence that there is a difference between mean response regarding preference for camping or fishing. (C)Fail to reject the null hypothesis, there is insufficient evidence that there is a difference between mean response regarding preference for camping or fishing. (D)Fail to reject the null hypothesis, there is sufficient evidence that there is a difference between mean response regarding preference for camping or fishing

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

(a) What is the level of significance? .05

State the null and alternate hypotheses.

H₀: ?₁ = ?₂; H₁: ?₁ ≠ ?₂

(b) What sampling distribution will you use? What assumptions are you making?

(A) The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations.

(B)The Student's t. We assume that both population distributions are approximately normal with known standard deviations.

(C)The standard normal. We assume that both population distributions are approximately normal with known standard deviations.

(D)The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.

What is the value of the sample test statistic? (Test the difference ?₁ − ?₂. Round your answer to two decimal places.)

Find (or estimate) the P-value. (Round your answer to four decimal places.)

Sketch the sampling distribution and show the area corresponding to the P-value. (if you can)

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ??

(A) At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(B)At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.

(C)At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

(D)At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.

(e) Interpret your conclusion in the context of the application.

(A) Reject the null hypothesis, there is insufficient evidence that there is a difference between mean response regarding preference for camping or fishing.

(B) Reject the null hypothesis, there is sufficient evidence that there is a difference between mean response regarding preference for camping or fishing.

(C)Fail to reject the null hypothesis, there is insufficient evidence that there is a difference between mean response regarding preference for camping or fishing.

(D)Fail to reject the null hypothesis, there is sufficient evidence that there is a difference between mean response regarding preference for camping or fishing.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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